We all remember Hippolyte Fizeau's famous 1849 speed-of-light experiment from sixth-grade science lessons. Through some byzantine combination of a mirror, a cigarette lighter, and a zoetrope he calculated that light must travel at 313,000 kilometers per second, remarkably close to the accepted measurement of 299,792.458 kmps. William Derham calculated the speed of sound in the early 1700's using a shotgun and a stopwatch (343 meters per second). But smells seem to be difficult measurement subjects. Children's television host Bill Nye attempts to explain:
The speed with which a smell travels depends on how fast the molecules are going, how massive they are, the relative temperature of the molecules making the smell, and how many molecules there are in a given volume, their density. We express all this mathematically as a gas's temperature and pressure.
Not good enough, Mr. Nye! I want numbers! PSI's vs. FPS's PDQ! Over at Yahoo Answers we find a more convincing explanation:
Smells are just chemicals. The speed that chemicals diffuse in the air is predicted by Graham's Law when you compare two gases.
Use oxygen as your standard gas.
The ratio of the speed of diffusion on the smell compared to oxygen is equal to the square root of the inverse of the mass of the oxygen molecule divided by the mass of the molecule of the smell.
The molecule of sulfur has 8 atoms of sulfur in each molecule, oxygen has two atoms per molecule. The mass of sulfur is 32 and oxygen is 16. The mass of their respective molecules are 8x32 and 2x16 or 256 and 32. Take the ratio of the two, oxygen over sulfur is 32/ 256 or 2^5/2^8 or 1/8. Take the square root of 1/8 is 0.354.
smell is about 1/3rd of the average speed of the molecules of oxygen in the air.
the speed of smell is smell is about 1/3rd of the average speed of the molecules of oxygen in the air.
YES! I'm generally willing to hedge my bets on the reliability of Yahoo Answers, typos and all, but what is the average speed of oxygen molecules in the air? I traipsed over to http://www.newton.dep.anl.gov to investigate:
So, if we take a 27° C room (a balmy 80.6° Fahrenheit), with air molecules moving at 500 m/s, the smell of a rotten egg travels at 166.66 meters a second! Is that FAST or WHAT!
There's a really neat mathematical equation based on a theorem called the "equipartition theorem" which states that the energy of a gas system (equal to 1/2*mv^2) is equal to the temperature of the gas (equal to 3/2*kT). If we rewrite this equation to solve for velocity we get:
sqrt(3*T*k/m) = v
where T is the temperature in Kelvin, k is the Boltzman constant = 1.3805*10^-23 J/K and m is the mass of the gas particle.
If we assume that the average mass of air (since it is a mixture of different gases) is 28.9 g/mol (or each gas particle is around 4.799*10^-26), and room-temperature is 27C or 300K, we find that the average velocity of a single air particle is around 500 m/s or 1100 miles per hour!
4 comments:
Yeah! You know how they say that sharks can smell your blood from like 2 miles away or something? I've always wondered about that. How is that even possible?
http://www.elasmo-research.org/education/topics/s_nose.htm
Also, nice picture. You can really tell that schnoz is sniffin'.
I had to throw 'zoetrope' into my dictionary widget, because I knew the image conjured of Zoe Deschanel, though adorable, was wrong.
I have the answer for Mr Dylan here but I'll never provide it. He's and you're all sinners.
Post a Comment